# Mazur’s structure theorem

Any normed associative real division algebra is isomorphic to one of the following:

• The real numbers $\mathbb{R}$.

• The complex numbers $\mathbb{C}$.

• The quaternions $\mathbb{H}$.

The next generalization, the octonions, often viewed as the “complexification” of the quaternions, fails to be associative.

Title Mazur’s structure theorem MazursStructureTheorem 2013-03-22 14:50:04 2013-03-22 14:50:04 mathcam (2727) mathcam (2727) 7 mathcam (2727) Theorem msc 11R52 TheoremsOnSumsOfSquares